We apologize for this difficulty you are experiencing. There are a few things you might want to try to speed things up a bit

1) Make sure there are no other programs or downloads running in the background while you are playing Build-A-Bearville. This makes your computer work double-time, thus making it run slow.

2) Sometimes things run slowly when a den is beary busy. For example, Friday afternoon is a popular time to log in to Build-A-Bearville. You might find that the game runs slowly then. Log in again, and this time, try clicking on a den that isn't quite as full of Guests as the others.

3) Check your computer for any signs of a virus or a spyware. You might want to ask help from your parents or guardian upon doing this.

I have the same issues. Right when it's my turn to pick what I want in trades the BSOD shows up and I have to log out and log back in. Or i'm going into a server and the BSOD shows up again. It happens all the time, I closed other web browsers and I know for a fact my computer is not infected since once a week I do a virus/spy-ware scan.
Curse you Black Screen Of Death! xD

I waited for about an HOUR because BABV wwouldn't load and the black screen came I waited and waited but it still didn't come (

The trick to logging in and avoiding the black screen is this:
click on a country ( any country)
Do not click a den yet!!
Wait ten seconds or until you see the spinning hour glass appear
Once the spinning hour glass disa ppears then click the den to enter bearville
I have been doing that for two months and it works every time!